http://prola.aps.org/abstract/PRL/v82/i21/p4352_1 Entropic Attraction and Repulsion in Binary Colloids Probed with a Line Optical Tweezer J. C. Crocker, J. A. Matteo, A. D. Dinsmore *, and A. G. Yodh Department of Physics and Astronomy, University of Pennsylvania, 209 S. 33rd Street, Philadelphia, Pennsylvania 19104 Received 15 June 1998 http://crocker.seas.upenn.edu/CrockerMatteo1999.pdf The long-range entropic forces that arise between two micrometer-sized colloidal spheres in a fluid of much smaller colloidal spheres were directly measured using a line-scanned optical tweezer. This new technique allowed us to measure the functional form of the potential with sub- kBT energy and 15 nm spatial resolution. At the lowest small sphere concentrations, the potential was monotonically attractive, while at higher concentrations an oscillatory potential was observed, due to the liquid structure of the small spheres. Surprisingly, the large spheres came together only rarely at the higher concentrations, suggesting a new means for stabilizing suspensions using entropy alone. Surprisingly, the large spheres came together only rarely at the higher concentrations, suggesting a new means for stabilizing suspensions using entropy alone. Entropic forces between macromolecules in suspension are often produced by the addition of smaller particles to the background solvent [1­11]. These forces have con- siderable technological importance ranging from protein crystallization to the reversible aggregation of industrial suspensions. At low concentrations of the small species, the forces are traditionally described by the depletion model of Asakura and Oosawa [1], which predicts a mono- tonically attractive potential, with a range given by the small species diameter. When the smaller particles are concentrated, however, their liquid-structural correlations can dramatically change the interaction to include a repul- sive or even oscillatory component [3]. as the small spheres are made more concentrated. We measured the interaction potential between an isolated pair of 1100 6 15 nm diameter PMMA (polymethylmethacry- late) spheres (Bangs Labs, Inc) induced by a background of smaller, 83 nm diameter PS (polystyrene) spheres (Ser- adyn, Inc). We varied the volume fraction of the small The measured large sphere pair potentials are presented in Fig. 1 for seven values of fS ranging from 0.04 to 0.42, as well as a control measurement with fS 0. The most prominent feature is a strong attraction at short range. An explanation of this attractive depletion force was first provided by the Asakura-Oosawa [1] (AO) theory, which assumes that the small spheres behave as an ideal gas. Around each large sphere there is a thin shell, or "depletion zone" (Fig. 2a), into which the centers of the small spheres cannot penetrate. When two large spheres approach each other, their depletion zones overlap, increasing the total volume accessible to the small spheres, increasing their entropy, and decreasing the system's free energy. http://crocker.seas.upenn.edu/CrockerMatteo1999.pdf Find a 2 kT bump at concn of 0.2 Wilson Poon [4] W. C. K. Poon and P. B. Warren, Europhys. Lett. 28, 513 (1994). Phase behaviour of hard-sphere mixtures http://www.iop.org/EJ/abstract/0295-5075/28/7/010 http://www.iop.org/EJ/article/0295-5075/28/7/010/epl_28_7_010.pdf R. Dickman, P. Attard, and V. Simonian, J. Chem. Phys. 107, 205 (1997); B. Götzelmann, R. Evans, and S. Deitrich, Phys. Rev. E 57, 6785 (1998); X. L. Chu, A. D. Nikolov, and D. T. Wasan, Langmuir 12, 5004 (1996); T. Biben, P. Bladon, and D. Frenkel, J. Phys. Condens. Matter 8, 10 799 (1996); J. Piasecki, L. Bocquet, and J. P. Hansen, Physica (Amsterdam) 218A, 125 (1995); Y. Mao, P. Bladon, H. N. W. Lekkerkerker, and M. E. Cates, Mol. Phys. 92, 151 (1997). R. Dickman, P. Attard, and V. Simonian Entropic Forces in Binary Hard-Sphere Mixtures: Theory and Simulation', J. Chem. Phys. 107, 205-213 (1997)